On Bicomplex Representation Methods and Applications of Matrices over Quaternionic Division Algebra

References

[1] L. X. Chen, “Inverse Matrix and Properties of Double Deter-minant over Quaternion TH Field,” Science in China (Series A), Vol. 34, No. 5, 1991, pp. 25-35.

[2] L. X. Chen, “Generaliza-tion of Cayley-Hamilton Theorem over Quaternion Field,” Chinese Science Bulletin, Vol. 17, No. 6, 1991, pp. 1291-1293.

[3] R, M. Hou, X. Q. Zhao and l. T. Wang, “The Double Determinant of Vandermonde’s Type over Quaternion Field,” Applied Mathematics and Mechanics, Vol. 20, No. 9, 1999, pp. 100-107.

[4] L. P. Huang, “The Determinants of Quateruion Matrices and Their Propoties,” Journal of Mathe-matics Study, Vol. 2, 1995, pp. 1-13.

[5] J. L. Wu, L. M. Zou, X. P. Chen and S. J. Li, “The Estimation of Eigenvalues of Sum, Difference, and Tensor Product of Matrices over Quater-nion Division Algebra,” Linear Algebra and its Applications, Vol. 428, 2008, pp. 3023-3033. doi:10.1016/j.laa.2008.02.008

[6] T. S. Li, “Properties of Double Determinant over Quaternion Field,” Journal of Cen-tral China Normal University, Vol. 1, 1995, 3-7. doi:10.1007/BF02652076

[7] B. X. Tu, “Dieudonne Deter-minants of Matrices over a Division Ring,” Journal of Fudan university, 1990A, Vol. 1, pp. 131-138.

[8] B. X. Tu, “Weak Direct Products and Weak Circular Product of Matrices over the Real Quaternion Division Ring,” Journal of Fudan Univer-sity, Vol. 3, 1991, p. 337.

[9] J. L. Wu, “Distribution and Estimation for Eigenvalues of Real Quaternion Matrices,” Computers and Mathematics with Applications, Vol. 55, 2008, pp. 1998-2004.
doi:10.1016/j.camwa.2007.07.013

[10] B. J. Xie, “Theorem and Application of Determinants Spread out of Self-Conjugated Matrix,” Acta Mathematica Sinica, Vol. 5, 1980, pp. 678-683.

[11] Q. C. Zhang, “Properties of Double Determinant over the Quaternion Field and Its Applications,” Acta Mathe-matica Sinica, Vol. 38, No. 2, 1995, pp. 253-259.

[12] W. J. Zhuang, “Inequalities of Eigenvalues and Singular Values for Quaternion Matrices,” Advances in Mathematics, Vol. 4, 1988, pp. 403-406.

[13] W. Boehm, “On Cubics: A Survey, Com-puter Graphics and Image Processing,” Vol. 19, 1982, pp. 201-226.
doi:10.1016/0146-664X(82)90009-0

[14] G. Farin, “Curves and Surfaces for Computer Aided Geometric Design,” Aca-demic Press, Inc., San Diego CA, 1990.

[15] K. Shoemake, “Animating Rotation with Quaternion Calculus,” ACM SIG-GRAPH, 1987, Course Notes, Computer Animation: 3–D Mo-tion, Specification, and Control.

[16] Q. G. Wang, “Quater-nion Transformation and Its Application to the Displacement Analysis of Spatial Mechanisms, Acta Mathematica Sinica, Vol. 15, No. 1, 1983, pp. 54-61.

[17] G. S. Zhang, “Commutativity of Composition for Finite Rotation of a Rigid Body,” Acta Mechanica Sinica, Vol. 4, 1982.

[18] E. T. Browne, “The Characteristic Roots of a Matrix,” Bulletin of the American Mathematical Society, Vol. 36, 1930, pp. 705-710.
doi:10.1090/S0002-9904-1930-05041-7

[19] J. L. Wu and Y. Wang, “A New Representation Theory and Some Methods on Quaternion Division Algebra,” Journal of Algebra, Vol. 14, No. 2, 2009, pp. 121-140.

[20] Q. W. Wang, “The General Solu-tion to a System of Real Quaternion Matrix Equation,” Com-puter and Mathematics with Applications, Vol. 49, 2005, pp. 665-675.
doi:10.1016/j.camwa.2004.12.002

[21] G. B. Price, “An In-troduction to Multicomplex Spaces and Functions,” Marcel Dekker, New York, 1991.

[22] D. Rochon, “A Bicomplex Riemann Zeta Function,” Tokyo Journal of Mathematics, Vol. 27, No. 2, 2004, pp. 357-369.

[23] S. P. Goyal and G. Ritu, “The Bicomplex Hurwitz Zeta function,” The South East Asian Journal of Mathematics and Mathematical Sciences, 2006.

[24] S. P. Goyal, T. Mathur and G. Ritu, “Bicomplex Gamma and Beta Function,” Journal of Raj. Academy Physical Sciences, Vol. 5, No. 1, 2006, pp. 131-142.

[25] J. N. Fan, “Determinants and Multiplicative Functionals on Quaternion Matrices,” Linear Algebra and Its Applications, Vol. 369, 2003, pp. 193-201.
doi:10.1016/S0024-3795(02)00722-X

[26] Q. W. Wang, “A System of Four Matrix Equations over Von Neumann Regular Rings and It Applications,” Acta Mathematica Sinica, Vol. 21, 2005, pp. 323-334.
doi:10.1007/s10114-004-0493-1

[27] Q. W. Wang, “A System of Matrix Equation and a Linear Matrix Equation over Arbi-trary Regular Rings with Identity,” Applied Linear Algebra, Vol. 384, 2004, pp. 43-54.
doi:10.1016/j.laa.2003.12.039

[28] W. J. Zhuang, “The Guide of Matrix Theory over Quaternion Field,” Science Press, Bei-jing, 2006, pp. 1-50.

[29] W. L. LI, “Quaternion Matrices,” “National Defense Science and Technology University,” Vol. 6, 2002, pp. 73-74.

[30] R. X. Jiang, “Linear Algebra,” People’s Educational Press, China, 1979, pp. 41-42.